Perfectly elastic collision problem with no given values

1. The problem statement, all variables and given/known data
A curling stone with initial speed vi1 collides head-on with a second, stationary stone of identical mass, m. Calculate the final speeds of the two curling stones.

2. Relevant equations
See attached picture

3. The attempt at a solution
I solved for vf1 as shown, but my answer was wrong. I got vi1-vf2=vf1, but the correct answer is vf1=0. What did I do wrong?

Please type your equations here, as the rules require, rather than uploading a picture. I have a very difficult time seeing anything you wrote in step 3, which is where you went wrong. It looks like you butchered your algebra, but I can hardly read it.

However, in general, to approach this problem, use the conservation of energy and the conservation of momentum. You'll then have a system of two equations and can solve for the velocities.

I second @RedDelicious ' remarks about postings, and note that BvU has said the same in another of your threads. Please bear in mind that although typing costs you a bit of time it will save time for the many people who read it.

For perfectly elastic collisions, it can save a lot of working to use a simple mass-independent result relating initial and final velocities. This relationship can be derived from the two conservation laws, but using it avoids the quadratics that come from conservation of energy.
Look up coefficient of restitution, and consider the case where it is 1.

I second @RedDelicious ' remarks about postings, and note that BvU has said the same in another of your threads. Please bear in mind that although typing costs you a bit of time it will save time for the many people who read it.

For perfectly elastic collisions, it can save a lot of working to use a simple mass-independent result relating initial and final velocities. This relationship can be derived from the two conservation laws, but using it avoids the quadratics that come from conservation of energy.
Look up coefficient of restitution, and consider the case where it is 1.

I just thought it would make more sense if I showed a picture of exactly what I did